Method for analyzing operation of a machine

ABSTRACT

A constraint analysis and reliability agent executes a method for analyzing operation of a manufacturing asset, and includes the steps of collecting operation data for a machine over a plurality of predetermined time periods. The operation data includes a plurality of mutually exclusive events that describe operation of the machine. For each of the predetermined time periods, it is determined whether the machine is in an “ON” or an “OFF” state. Data for the “OFF” states is removed from the collected data to generate a filtered data set. Reliability information is then generated based, at least in part, on the filtered data set. This facilitates predictions of future machine operation.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a method for analyzing operation of amachine, and in particular, a method of reliability and constraintanalysis for a machine.

2. Background Art

Recently, Factory Information Systems (FIS's) have become an importanttool in automotive manufacturing. They can provide important informationabout the operation of various “assets”, such as robots, conveyordrives, weld guns, pumps, or other equipment used in manufacturing. Atypical automotive FIS is based on a three layer informationarchitecture, including a lower layer of asset controlling programmablelogic controllers (PLC's), an intermediate layer of transfer PLC's, anda layer of servers that are accessible from an office automation (OA)network. Each of the asset controlling PLC's sends to a respective oneof the transfer PLC's a standard package of data blocks. These datablocks can include, for example, data related to some or all of thefollowing: cycle time, blocked time, starve time, downtime, faultvectors, and machine process parameters.

It is generally understood that cycle time includes the time duringwhich a machine is performing its intended manufacturing operation, suchas rotating, welding, stamping, spraying, etc., or it is in the processof preparing to do so—e.g., a portion of it is moving from one positionto another, or it is changing tools. Conversely, a “blocked time” is atime during which the machine is forced to be idle because the nextmachine in the work cell or line is not ready to receive another part. Asimilar situation occurs when the prior machine in the work cell or linehas not finished its operations, and therefore has no parts to transferto the machine under analysis: in such a case, the machine is “starved”.“Downtime” can occur for any number of reasons, including tool breakage,machine failure, etc. As noted above, the data blocks can also includeprocess parameters, which can include such information as standard cycletimes, tool changes, number of operations, etc.

In the model discussed above, the transfer PLC's in one area may belinked in a virtual local area network (VLAN) with a gateway personalcomputer (PC) that isolates the lower layer of controlling PLC's fromthe OA net. The data for each area is organized in a database and storedon a server that is OA accessible. This architecture is the foundationof a web enabled FIS that allows for monitoring the operating attributesof the critical assets that are controlled or monitored by the PLC. Anumber of commercially available FIS's are commonly used in automotivemanufacturing plants.

Despite providing some benefits over manual data collection,conventional FIS's are passive systems that produce predefined reports,and have limited analytical, modeling, and prognostic capability. Thesesystems operate as a decision supporting tool, rather than a proactivealgorithmic instrument that can autonomously implement and optimize someof the traditionally manual activities like evaluation of data integrityand feasibility, equipment reliability assessment, bottleneck constraintanalysis, etc.

Therefore, a need exists for a method for automatically implementing atleast some of these activities, for example, through an automaticreliability and constraint analysis agent that can be applied in amanufacturing environment to facilitate prediction of future machineoperation.

SUMMARY OF THE INVENTION

Accordingly, the present invention provides a constraint analysis andreliability agent for implementing a method for analyzing operation amachine or group of machines. Embodiments of the invention can includemethod steps for one or more of the following:

(a) automatic filtering of outliers and inferring plant schedule basedon the state of the assets,

(b) automatic evaluation and/or prediction of the survival probabilityof available assets,

(c) automatic on-line learning from the data of the type and parametersof probability distributions for the “time-to-failure” (TTF) and“time-to-repair” (TTR),

(d) automatic constraint analysis for all modeled lines of equipment,

(e) automatic sensitivity analysis of identified constraints, and

(f) automatic prioritization of preventive maintenance based on thebottleneck constraints and survival probability of the assets.

With regard to the first of these features—i.e., automatic filtering ofoutliers and inferring plant schedule based on the state of theassets—the present invention can perform a number of steps to increasethe accuracy of the information generated for machine reliability andconstraint analysis. For example, a conventional FIS assumes that anaccurate and regularly updated schedule of plant operation is available.In reality, this assumption is not always true, especially in cases whenunscheduled breaks and outages occur, or the person responsible forupdating the schedule is not available. In order to avoid inaccuracies,the present invention provides a method for continuously analyzing thestate of the individual assets, and infers the actual schedule based onthe actual data reported by the base FIS.

One feature of the automatic identification of the plant schedule isbased on the fact that if a production line is in a normal operatingmode, then most of the assets change their state—e.g., cycle, block,down, starve—frequently. It is worth noting that the above four statesare not the only ones that can be used with the present invention.Indeed, depending on the machine or machines under analysis, it may bedesirable to use different states. It should be considered, however,that to learn an accurate machine schedule, the set of states underconsideration should be mutually exclusive, and should completely definethe operation of the machine.

One algorithm for inferring the schedule follows the following logic:

(a) each day is split into multiple time blocks—e.g., a 24 hour periodmay be split into 288 blocks of 5 min each,

(b) for each time block, if an asset has multiple cycle, block or starveinstances, the asset is “ON”; otherwise, it is “OFF”, and

(c) for each time block, if most of the assets (in the same line orgroup) are ON, the line is ON; otherwise, the line is OFF.

The result of application of the above rules provides a filtered dataset that can be expressed as a table, called an “evidence table”. Thistable indicates whether each asset or line is operating (denoted with a“1”) or is not operating (denoted with a “0”). The evidence table can befurther refined by eliminating unnecessary data. A more compact form isobtained by combining blocks with same state and saving only ON or OFFblocks. It is readily understood that if, for example, only the OFFblocks are saved, all non-saved blocks must be ON blocks; therefore,there is no need to separately store this data.

The finalized group evidence table contains the actual time when theparticular line or group has been OFF. The evidence table for each groupor line can be, for example, calculated on a daily basis and stored. Theevidence table can be further used for filtering the outliers. That is,if certain data values, such as cycle times, are significantly differentthan the mean cycle time for an asset, and have low frequencies, theywill be eliminated. The evidence table can also be used to obtainparameters related to asset reliability, such as TTF and TTR data.

As noted above, embodiments of the present invention also provide forautomatic evaluation and/or prediction of the survival probability ofavailable assets. Survival functions can be a practical tool forestimating the remaining useful lifetime of a machine, since in essence,they give the probability that a machine is in proper working order atany given time. After enough time has passed, the survival probabilitywill drop to zero, representing a complete and fatal breakdown of themachine.

Different embodiments of the present invention may apply differentmethodologies to generate an appropriate survival function for an asset.In some embodiments, for example, the data is fit to a Weibulldistribution survival function that is estimated for the entirepredicted lifetime of the machine. In other embodiments, for example,the data is fit recursively to a linear regression model that predictsthe new survival probability one step ahead, and constantly updatesitself as each new data point is observed.

To implement the survival probability analysis described above, thepresent invention may use a survival function takes the general form:S=f(t),where (S) is called the survival probability, and f(t) is some functionof time. In some embodiments, (t) can be the cumulative operating timeto fail (OTTF). Operating time is defined as time that a machine is notin a faulted state. In other words, it is the time that the machine iscycling (carrying out its intended job), starved, or blocked. For anygiven machine's data set, a new OTTF is calculated as the total amountof operating time occurring prior to each individual failure of themachine. These OTTF values are then used as the (t) values when fittingthe data to an appropriate survival function f(t).

In these embodiments of the present invention, (S) can be, for example,the cumulative survival rate, or the percentage of overall time that amachine had been in a non-faulted state up to that point. This can becalculated by taking the ratio of the OTTF to the sum of the OTTF andthe cumulative time spent repairing the machine (TTR):

$\begin{matrix}{S = \frac{OTTF}{{OTTF} + {TTR}}} & {{Eq}.\mspace{14mu} 1}\end{matrix}$For any given machine's data set, a new (S) value is calculated afterthe repair of any given failure of the machine.

As noted above, the present invention may use a probability densityfunction, such as a Weibull distribution, to help predict survivalprobability. The probability density function (PDF) of the two-parameterform of the Weibull distribution is defined as:

${f\left( {t,\alpha,\beta} \right)} = {\frac{\beta}{\alpha}\left( \frac{t}{\alpha} \right)^{\beta - 1}{\exp\left( {- \left( \frac{t}{\alpha} \right)^{\beta}} \right)}}$where (t) is time. The dimensionless shape parameter is (β) and thescale parameter having the units of time is (α). The survival functionfor the Weibull distribution is the exponential portion of its PDF, andis therefore given by:

${S\left( {t,\alpha,\beta} \right)} = {\exp\left( {- \left( \frac{t}{\alpha} \right)^{\beta}} \right)}$Before data can be fit to it, this equation must be converted to alinear form, which can be done by taking the double natural log of bothsides:ln(−ln[S(t,α,β)])=βln t−β ln αAs a result, a recursive linear least square techniques (RLS), or, forexample, use of a Kalman filter, is applied to estimate in real time theparameters of the survival function:

${\ln\left( {- {\ln\left\lbrack \frac{OTTF}{{OTTF} + {TTR}} \right\rbrack}} \right)} = {{\beta\;\ln\;{OTTF}} - {\beta\;\ln\;\alpha}}$This model also provides the probability that the machine will be in afaulted state after some given amount of operating time, since theprobability of failure is one minus the survival rate.

Also discussed above is that embodiments of the present invention mayprovide automatic on-line learning of the type and parameters of TTF andTTR probability distributions. Unlike conventional simulation packagesthat assume either default TTF and TTR distributions—e.g., Exponentialor Erlang distributions—or estimate the distributions by fittinghistorical data, the present invention provides implementations of aconstraint analysis algorithm that takes advantage of the fact thatinformation from the on-line updated FIS database is available. Thisallows the use of an algorithm that periodically evaluates and updatesthe TTF and TTR distributions with respect to the data collected by theFIS.

In order to evaluate and update the TTF and TTR distributions, theparameters of a number of TTF and TTR probability distributions areexamined. In some embodiments of the present invention, the followingeight distributions are examined: Weibull, Gamma, Exponential, Rayleigh,Poisson, Normal, Lognormal, and Erlang. The Kolmogorov-Smirnov (K-S)test is applied evaluate the compatibility of collected data and thedistributions.

In order to avoid frequent switching of probability distributions, adecision algorithm is used to assess the validity of the learneddistributions on a validation data subset that is randomly selected, andthat is not used for fitting. The recently adopted distribution (in thevery start of the algorithm the Exponential and Erlang distributions areconsidered as defaults) are stored in a database and are used asdefaults. They are replaced only in cases where they are significantlyover-performed by the newly learned probability distributions.

As discussed above, embodiments of the present invention also provide amethod for constraint analysis, sensitivity analysis, and automaticprioritization of preventive maintenance. These features are nowsummarized. Traditional Constraint analysis tools are typicallyheuristic tools using the dominate state of the machine—e.g., downtimeor a balance of block and starve conditions—to identify the constrainingmachine or operation in a production line or system. Although thismethod may correctly identify the constraining machine or operation, itcan be easily “fooled” when several machines with different operatingparameters are in the same production line or system (group).

Similarly, when multiple machines or operations combine to form avirtual bottleneck, such traditional approaches cannot identify suchcombinations. Embodiments of the present invention use a heuristic toidentify a list of likely candidate constraints, then run simulationexperiments to determine the impact of each candidate on the productionrate of the line or system. The likely candidate list is derived byfirst identifying the “worst” performing machine in the group, thenidentifying all other machines in the group that are within a fixedpercent of the worst machine. Additional intelligence can be added toidentify any other likely candidates if desired. This selection issummarized as follows:

If Mi (i=1, 2, . . . N) is a list of machines in a group, and (ci, di,bi, si) are (Percent cycling, percent down, percent blocked and percentstarved, respectively), then define w=the index of the “worst” machinegiven by:w=Max(ci+di)(1≦i≦n)   Eq. 2and the Candidate set L={i|(cw+dw}−(ci+di)<δ}, where δ=a fixed percent(i.e., 5% or 10%). Let m=the number of elements of set L.

Then, an ad hoc design of experiments (DOE)—or any standard DOE such asfull partial factorial designs—can be used to test each candidate inisolation or in combination as to the impact on throughput of making animprovement to that machine or operation. For example, three types ofimprovements that may be considered are: improved cycle time—e.g.,ci′=0.95*ci, improved downtime—e.g., adjusting TTF distributionparameters such that a new mean time-to-failure (MTTF′) is greater thana baseline mean time-to-failure (MTTF): MTTF′=1.05*MTTF, and adding orincreasing buffers before and after the machine or group. The latter maytake the form of increasing buffer size by either a standardamount—e.g., 10 units—or setting the buffer to a value greater than somefactor of a mean time-to-repair (MTTR): 2*MTTR/ci.

After completing the sensitivity analysis outlined below, beginning withthe results of the single machine constraint analysis, and based on theresults of the DOE, the set L can be ordered from highest impact tolowest. An alternative is to use the values of (ci+di) directly tocreate the order. If desired, additional machines and/or operations canbe added to the set using the procedure above to estimate the potentialimpact of that machine and/or operation. Given the ordered list, andstarting with the two highest impact machines, a simulation can be runwhere both machines are changed—choosing the best parameter to changefor each machine.

Next, a third machine is added to the first two machines, and thesimulation is rerun. This process is continued until no additionalincremental improvements are seen. Alternatively, the simulation can becontinued with one or two additional machines, and if no significantimprovement is seen, a prior improvement state can be used. This helpsto ensure that the simulation algorithm does not end prematurely. Thismethod provides a sequential order in which to make improvements.

Embodiments of the present invention can also perform automaticsensitivity analysis of identified constraints. For example, one DOE isto run the simulation model 3*(m+1) times for each group, plus run itfor a base case, wherein all machines are set to an “as observed”condition. The first m+1 runs are performed to change each machine'scycle time as indicated, one at a time, and then a final run isperformed where all machines in the group are changed together.

The second m+1 runs follow the same pattern, but the downtime is changedinstead of the cycle time. The third group follows the same pattern forbuffers before each machine or operation, after each machine oroperation, or both. By performing a comparison with the base, theindividual machine changes, and the group change results, it is possibleto identify if a true single bottleneck exists, or if the bottleneck ismultiple machines in combination. This method can give three differentbottlenecks, one with respect to each of the three parameters—i.e.,cycle time, downtime or decoupling/buffering—potentially giving theplant some options regarding productivity improvements. For a completesensitivity analysis, the same set of runs is performed, but theparameter is changed to increase instead of decrease.

Automatic prioritization of the preventive maintenance may take place asfollows. After a scheduled execution of the method of the presentinvention, which can be specified, for example, as a weekly or monthlytask on a hosting server, each asset is assigned a constraint rank withrespect to the line or cell in which it operates. The higher the rankis, the more likely it is the modeled line's constraining asset duringsimulation.

The automatic prioritization of preventive maintenance is performed bygoing through all of the available assets seeking those having bothrelatively low predicted survival probabilities and high constraintranks within their parent lines. Assets showing traits matching both ofthese criteria should be assigned a higher priority to have theirmaintenance activity performed than those that do not have those traits.The capability to produce this list is integrated within the agent usedto implement the method of the invention, and the list is updated aftereach its execution.

Assets that make the list are those with lower reliability and which aredragging down performances of their parent lines. Maintenance schedulesand priorities can be adjusted by using the list to make informeddecisions to maximize the efficiency and the limited resources of themaintenance group. At the same, utilizing the list can lower risks ofunanticipated machine failures.

The present invention also provides a method for analyzing operation ofat least one machine. The method includes collecting operation data fora machine over a plurality of predetermined time periods. The operationdata includes the respective time for a plurality of events thattogether form a set of mutually exclusive events that describe operationof the machine. For each of the predetermined time periods, it isdetermined whether the machine is in an on” state or a “off” state basedat least in part on the collected operation data. Data for the OFFstates is removed from at least a portion of the collected operationdata, thereby generating a filtered data set. Reliability information isgenerated for the machine based at least in part on the filtered dataset. This facilitates predictions of future machine operation.

The invention further provides a method generally as given above, but inwhich the set of events includes cycle events, starve events, blockedevents, and down events. The step of generating reliability informationincludes determining a time-to-failure parameter using at least the downevents from the filtered data set. It also includes determining atime-to-repair parameter using at least the down events from thefiltered data set, and choosing a probability density function. Thedetermined parameters are then fitted to the chosen probability densityfunction to generate reliability information for the machine.

The invention also provides a method for analyzing operation of aplurality of machines. The method includes collecting operation data foreach of the machines over a plurality of predetermined time periods. Theoperation data for each machine includes the respective time for aplurality of events that together form a set of mutually exclusiveevents that describe operation of the respective machine. For each ofthe predetermined time periods it is determined whether each machine isin an ON state or an OFF state based at least in part on the collectedoperation data for the respective machine. Data for the OFF states isremoved from at least a portion of the collected operation data, therebygenerating a filtered data set. Reliability information is generated foreach machine based at least in part on the filtered data set. Thisfacilitates predictions of the future operation of each machine. Thereliability information can then be used to perform a constraintanalysis for the machines.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a schematic representation of a Factory Information Systemin communication with a number of manufacturing assets and a computerconfigured to run a constraint analysis and reliability agent forperforming a method of the present invention;

FIG. 2 shows a flowchart illustrating a method of the present invention;

FIG. 3 shows a series of data tables constructed using a method of thepresent invention;

FIG. 4 shows a schematic diagram of a data filtering process inaccordance with a method of the present invention;

FIG. 5 shows a flowchart illustrating the steps of choosing aprobability density function in accordance with a method of the presentinvention;

FIG. 6 shows data filtered in accordance with a method of the presentinvention closely fit to a Weibull probability density function;

FIG. 7 shows a table with eight probability density functions and theirassociated parameters generated in accordance with a method of thepresent invention;

FIGS. 8A and 8B show graphs illustrating predicted survival functionsfor a manufacturing asset, generated in accordance with a method of thepresent invention; and

FIG. 9 shows a flowchart illustrating a constraint analysis andsensitivity routine in accordance with a method of the presentinvention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT(S)

FIG. 1 shows a schematic representation of a factory information system(FIS) 10 in communication with a number of manufacturing assets 12, suchas robots, conveyor drives, weld guns, etc. The FIS 10 is a three-layersystem with the first layer 14 including a number of PLC's 20, 20′, 20″.As shown in FIG. 1, the PLC's 20 are used to control manufacturingassets in a body shop. Similarly, the PLC's 20′ are used to controlassets used in a paint shop, and the PLC's 20″ are used to controlassets used in a final assembly (FA) shop. The same nomenclature usingthe prime and double prime symbols is used throughout the description ofthe FIS 10 to indicate similar components used in the differentmanufacturing areas.

The FIS 10 also includes an intermediate layer 16 of transfer PLC's 22,22′, 22″, each of which is connected to a respective personal computer24, 24′, 24″. Each of the computers 24, 24′, 24″ is in communicationwith a respective one of the asset controlling PLC's 20, 20′, 20″. Eachof the transfer PLC's 22, 22′, 22″ are in communication with arespective gateway computer 26, 26′, 26″ located in a third layer 18 ofthe FIS 10. Each of the gateway computers 26, 26′, 26″ is connected toan office automation (OA) network 29 that includes a respective servercomputer 28, 28′, 28″ for each of the manufacturing areas.

Also shown in FIG. 1 is a computer 30 that is configured to run aconstraint analysis and reliability agent for performing a method of thepresent invention. The agent can be programmed into software containedon the computer 30, or it can be written to hardware in the computer 30,or some combination of software and hardware. The computer 30communicates with the FIS 10, and in particular, with the network 29.

FIG. 2 shows a flowchart 32 illustrating a method in accordance with thepresent invention. As noted above, this method can be executed, forexample, by the computer 30 shown in FIG. 1. Object 34 in FIG. 2 is adatabase which may, for example, reside on an FIS server, such as theserver 28 shown in FIG. 1. At step 36, the method accesses from thedatabase 34 raw data, including times and operating states for theassets under analysis. In the embodiment shown in FIG. 2, step 36 is rundaily, though other frequencies may be used. As described above, thetimes and states for the various manufacturing assets may include a setof states having mutually exclusive events that completely describeoperation of the asset being considered. One such set includes the timesfor cycle events, starve events, blocked events, and down events. Theseevents are observed over a plurality of predetermined time periodswhich, for example, may be 288 five minute blocks to define a 24 hourday.

After the data is retrieved at step 36, an evidence table is created atstep 38. As shown in FIG. 2, the evidence table provides an actualschedule for the manufacturing asset under consideration, which helps toprovide accurate data for the reliability and constraint analysis tofollow. Each of the following steps are introduced in the flowchart 32,and are described in more detail below. After the evidence table isgenerated at step 38, a temporary database 40 is propagated with afiltered data set that includes time-to-failure and time-to-repair data.The filtered data set is generated by removing OFF states from the rawdata.

Using the information from the database 40 allows a reliability agentsystem to be implemented at step 42. Alternatively, the database 40 canbe used to generate information regarding the mean time-to-failure(MTTF) and the mean time-to-repair (MTTR) probability distributions—seestep 44. In the embodiments shown in FIG. 2, step 44 is implemented on aweekly basis, though other frequencies may be used. At decision block46, the decision is made whether the probability density function usedto describe the filter data should be updated, or whether the defaultdistribution should be used. At step 48, a constraint analysis isperformed, and data is output to a constraint analysis and reliability(CA&R) database 50. The CA&R database 50 also receives information fromthe reliability agent system 42. It is from the database 50, that aviewer can retrieve information regarding the constraints and thecritical assets in the manufacturing system under consideration—see step52.

FIG. 3 shows the progression of generating the evidence table inaccordance with step 38 shown in FIG. 2. FIG. 3 includes four differentdata tables 54, 56, 58, 60. Table 54 shows one example of time blocksthat can be used in accordance with the present invention. For example,in the embodiment shown in FIG. 3, a plurality of six minute intervalsare used to describe a longer time period, such as a shift, or an entireday.

The table 56 provides information regarding the production state changesfor each of eleven different assets. As shown in FIG. 3, for time blocks49-59, each of the eleven assets had only a single production statechange. This means that each of the assets had only a single change ofstate between a cycle event, starve event, blocked event, or down event.In the embodiment shown in FIG. 3, a single change in production stateover the predetermined time increment is considered an indication thatthe asset is in an OFF state. This is indicated in Table 58, which showsa zero for each of the eleven assets during each of the time blocks49-59. Conversely, Table 56 shows that for some of the assets, more thanone production state change occurred during time blocks 60-70. In such acase, the asset is considered to be in an ON state, which is indicatedin Table 58 by the numeral 1.

The group evidence table 60 further consolidates data by examining theeleven assets as a group, rather than individually. In a productionsetting, the eleven assets may each be in the same production line, theymay be part of a work cell, or some other configuration in which theywork together in a manufacturing process. In the embodiment of thepresent invention shown in FIG. 3, the asset evidence table is observedfor each time block, and if during an individual time block a majorityof the assets are in an ON state, then the group of assets is consideredto be ON, which is indicated by the numeral 1 in Table 60. Conversely,if less than half of the assets are in an ON state—see e.g., time block61—then the group is considered to be in an OFF state, which isindicated by a zero in the group evidence Table 60. Thus, theconsolidated group evidence table 60 provides at a glance informationregarding whether all of the eleven assets was ON or OFF during any ofthe time blocks.

FIG. 4 is a schematic diagram generally illustrating the generation ofthe database 40 shown in FIG. 2. As shown in FIG. 4, cycling information62 has removed from it information related to a special productionstate: “In Auto And Maint.” 64. The “In Auto And Maint.” is an automaticmode in which the machine or station is in a maintenance mode. Forexample, if the machine automatically generates a warning signal uponthe occurrence of a fault event, and the operator acknowledges thewarning, the machine or station is considered “In Auto And Maint.” Afterremoval of the “In Auto And Maint.”, for example, when the fault hasbeen eliminated, filtered cycling data 66 remains.

Similarly, cycling data 68 has removed from it data related to “In AutoAnd Faulted”. The “In Auto And Faulted” information is similar to the“In Auto And Maint.”, but in this mode, the operator has not yetacknowledged the warning. After the “In Auto And Faulted” data 70 isremoved from the cycling data 68, filtered cycling data 72 remains.Table 74 shows a summary of this filtering process wherein the cyclingdata of blocks 62, 68 have removed from them outlier data entries 76,78.

In addition to the filtering process removing data related to “In AutoAnd Maint.” and “In Auto And Faulted”, the present invention alsofilters out data related to the asset being in an OFF state. Thus, block80 shows all of the data including cycle, blocked, starve, and downdata, taken from the assets under consideration. Block 82 shows removalof data related to OFF production, which can be gleaned from theevidence table, for example, as shown in FIG. 3. What remains from thecombination of filtering the OFF production data and the “In Auto AndMaint.” and “In Auto And Faulted” is shown as the filtered data set 84.An additional filtering can take place, such as that shown in Table 86.In Table 86, outlier data 88, 90 is removed from the Table 86 to providemore accurate information when generating the Table 92.

The Table 92 shows reliability parameters TTF and TTR for two differentnode ID's for a number of different dates. The node ID is used toidentify a specific asset. As described above, the reliabilityparameters TTF and TTR can be mathematically combined, for example, asin equation 1, to create another reliability parameter that can be usedin a probability density function to facilitate predictions regardingfuture operation of the asset under consideration. Embodiments of thepresent invention fit the reliability parameters to a number ofdifferent probability density functions, and then choose one of theprobability density functions based on the compatibility of the data tothe function.

FIG. 5 shows a flowchart 94 illustrating the steps of choosing aprobability density function in accordance with the present invention.At decision block 96, it is decided whether the sample size availablefrom the data is greater than or equal to 50. If it is not, theflowchart moves to step 98, where the default distribution is used. Forsome embodiments of the present invention, either an exponential orErlang probability density function may be used as the defaultdistribution. If, however, the sample size is greater than 50, at step100, the method randomly divides the TTF and TTR data into training andvalidation subsets. As step 102, eight different probability densityfunctions are fit with data from the training subsets. Of course,greater or fewer than eight distributions can be used in differentembodiments of the present invention. For the embodiment illustrated inFIG. 5, the eight probability density functions used are: Weibull,gamma, exponential, Rayleigh, Poisson, normal, lognormal, and Erlang.

At decision block 104, it is determined whether the default distributionis available—i.e., whether data has been previously fit to adistribution. If a default distribution is not available, step 106 usesthe exponential and Erlang distributions as defaults, using the one ofthese two distributions that best fits the data in the training subset.If, however, at decision block 104 it is determined that a defaultdistribution is available, then distributions with an attainedsignificance level, or p-value, greater than or equal to 0.05 are chosenas candidate distributions—these will be used with the validationsubset. At step 110, a K-S test is used to determine the best fit amongthe probability density function candidates to be used as the finalcandidate distribution. Again, this will be used on the validationsubset of the data.

At decision block 112, it is determined whether a final candidatedistribution is available. If it is not, the method loops back to step98, and the default distribution is used. Conversely, if the finalcandidate distribution is available, another decision is made atdecision block 114. Here, it is determined whether the defaultdistribution has a p-value greater than 0.05. If it does not, the finalcandidate distribution then becomes the default, and the final candidatedistribution is used in a simulation.

If, at decision block 14, it is determined that the default distributiondoes have a p-value greater than 0.05, it is next determined at decisionblock 118 whether there is a significant mean shift between the defaultand the final candidate distributions. If not, the method loops back tostep 98, and the default distribution is used. Conversely, if there is asignificantly mean shift, the method loops back to step 116, and thefinal candidate becomes the default and is used in the simulation.

FIG. 6 shows a Table 120 indicating each of the eight differentprobability density functions, along with their associated parameters.Applying the K-S test to each of these probability density functionsyields the p-value column on the right of Table 120. As described above,it is desirable to use probability density functions having a highp-value. To the extent that a default distribution has a p-value greaterthan 0.05, it will be used so that the probability density function isnot changed with an undesirably high frequency. As noted above, with thefirst set of data fitted to a probability density function, either theexponential or Erlang distributions are used as a default. FIG. 7 showsa graph 122 of an initial fitting of a set of raw data to an exponentialprobability density function. Although the graph 122 is useful to showthe close correlation between the raw data and the probability densityfunction chosen, it does not present the data in a form that helps toindicate the reliability of the asset, or predict future behavior.

FIGS. 8A and 8B show two graphs 119, 121, in which a real survivalprobability has been graphed against predictions made 50 hours ahead.These graphs were generated using filtered data to determine a set ofreliability parameters—e.g., a mathematical combination of TTF andTTR—that was then fit to a probability density function and graphed. Thegraph 119 is based on a transformed Weibull probability densityfunction, while the graft 121 is based on an Evolving Takagi-Sugeno(ETS) model, though other models could be used. The graphs 119, 121 haveincluded the real survival probability to illustrate the closecorrelation between the predicted reliability determined using thepresent invention, and the actual reliability.

In addition to reliability data, the present invention also providesinformation related to system constraints—e.g., manufacturing assetswhich alone or in combination create a bottleneck. FIG. 9 shows aflowchart 124 illustrating the steps of a constraint and sensitivityanalysis in accordance with the present invention. As indicated at block126, the constraint analysis is begun and the baseline statistics aregathered from a simulation in block 128. In the embodiment shown in FIG.9, the simulation is run daily per asset group. At step 130, it isdetermined for each asset the percent of time it is down. Of course, oneminus this value represents the amount of time the asset is up. At step132, the “worst” machine is identified, for example, as described aboveusing equation 2. Also at step 132, all of the machines within 5% of theworst machine are also identified.

To improve the performance associated with these machines, one parameterthat can be adjusted is the cycle time—see step 134. After an adjustmentto the cycle time, the method of the present invention is applied againto generate new data, and the results are captured—see step 136. Theupdated results are then put in a database 138. Another parameter thatcan be adjusted is the mean time-to-failure of the worst machines. Atstep 140, this value is adjusted by 5%. The method then loops back tostep 136, where the method is again applied to generate new data andupdate the database at 138. A third parameter which can be adjusted isto add or increase the buffer between the worst machines and adjacentmachines. This is indicated in step 142. After this adjustment is made,the method again loops back to step 136 where the method is appliedagain to generate new data.

As indicated in the flowchart 124 in FIG. 9, this sensitivity analysisis iterative, and provides a mechanism for reducing the constraints in amanufacturing line or work cell. Of course, it is contemplated that themethod of the present invention can be run virtually continuously toprovide data that is constantly updated to indicate changes in thereliability of various manufacturing assets, and to gauge the effect ofmodifying certain operating characteristics, such as indicated at steps134, 140, 142 in FIG. 9. Thus, by ranking each of the machines, forexample, according to equation 2, and then identifying a group of theworst machines, bottlenecks within the manufacturing line can be easilyidentified so that improvements can be made. Moreover, determining theexpected reliability for the various manufacturing assets, such asillustrated in FIGS. 8A and 8B, provides a mechanism for predictingfuture operation of the assets, thereby helping to eliminate constraintsprior to their occurrence.

While embodiments of the invention have been illustrated and described,it is not intended that these embodiments illustrate and describe allpossible forms of the invention. Rather, the words used in thespecification are words of description rather than limitation, and it isunderstood that various changes may be made without departing from thespirit and scope of the invention.

1. A method for analyzing operation of at least one machine, comprising:collecting operation data for a machine over a plurality ofpredetermined time periods, the operation data including the respectivetime for a plurality of events that together form a set of mutuallyexclusive events that describe operation of the machine, the set ofevents including cycle events, starve events, blocked events, and downevents; determining for each of the predetermined time periods whetherthe machine is in an “ON” state or an “OFF” state based at least in parton the collected operation data; removing data for the OFF states fromat least a portion of the collected operation data, thereby generating afiltered data set; and generating reliability information for themachine based at least in part on the filtered data set, therebyfacilitating predictions of future machine operation, the step ofgenerating reliability information including: determining a reliabilityparameter based at least in part on the down events in the filtered dataset; choosing a probability density function; and fitting thereliability parameter to the chosen probability density function.
 2. Themethod of claim 1, wherein the machine is considered to be in an ONstate for a given one of the predetermined time periods when there ismore than one occurrence of a cycle event, a starve event, a blockedevent, or a combination thereof during the given predetermined timeperiod.
 3. The method of claim 1, wherein the step of determining thereliability parameter includes: determining a time-to-failure parameter;determining a time-to-repair parameter; and mathematically combining thetime-to-failure parameter and the time-to-repair parameter to generatethe reliability parameter.
 4. The method of claim 1, further comprising:collecting additional operation data for the machine; determining whenthe machine is in an ON state and when the machine is an OFF state;removing data for the OFF states from the additional operation data forthe machine and updating the filtered data set; determining when afailure of the machine has occurred; determining a time-to-repair thefailure; determining a new reliability parameter from the updatedfiltered data set; performing an analysis to determine compatibilitybetween the new reliability parameter and a plurality of probabilitydensity functions, thereby generating a plurality of compatibilityvalues; fitting the new reliability parameter to the probability densityfunction having the best compatibility value when the difference betweenthe best compatibility value and the compatibility value for the chosenprobability density function is greater than a predetermined amount; andfitting the new reliability parameter to the chosen probability densityfunction when the difference between the best compatibility value andthe compatibility value for the chosen probability density function isnot greater than the predetermined amount.
 5. The method of claim 1,further comprising: defining a work area having a plurality of machines;collecting corresponding operation data for the machines over thepredetermined time periods, the operation data including the time forcycle events, starve events, blocked events, and down events for eachrespective machine; determining for each of the machines over each ofthe predetermined time periods whether the respective machine is in anON state or an OFF state based at least in part on the respectivecollected operation data; removing data for the OFF states from at leasta portion of the corresponding collected operation data for eachmachine, such that the filtered data set includes information for eachmachine; and generating reliability information for each machine basedat least in part on the filtered data set, thereby facilitatingpredictions of future operation of each machine.
 6. The method of claim5, wherein the step of generating reliability information for eachmachine includes: determining a reliability parameter for each machinebased at least in part on the down events for the respective machine inthe filtered data set; choosing a corresponding probability densityfunction for each machine; and fitting each of the reliabilityparameters to the respective chosen probability density function.
 7. Themethod of claim 5, further comprising: determining for each of thepredetermined time periods whether the work area is in an ON state or anOFF state based at least in part on whether the machines in the workarea are in an ON state or an OFF state, the work area being consideredto be in an OFF state for a given one of the predetermined time periodsif a predetermined percentage of the machines in the work area aredetermined to be in an OFF state during the given predetermined timeperiod.
 8. The method of claim 7, further comprising removing additionaldata from at least a portion of the collected operation data to generatethe filtered data set, the additional data removed including data forthe ON states of the machines during a given one of the predeterminedtime periods when the work area is determined to be in an OFF state forthe given predetermined time period.
 9. The method of claim 8, furthercomprising performing a constraint analysis using the reliabilityinformation generated for each of the machines, thereby facilitatingidentification of bottlenecks within the work area.
 10. The method ofclaim 8, wherein the step of performing a constraint analysis includes:identifying the machine having the greatest percentage of downtime;identifying at least one other machine having a percentage of downtimewithin a predetermined amount of the greatest percentage of downtime;and analyzing the impact on throughput for each of the identifiedmachines, thereby providing information for reducing constraints. 11.The method of claim 1, further comprising: determining for each of thepredetermined time periods whether the machine is in an “auto andmaintenance” state; determining for each of the predetermined timeperiods whether the machine is in an “auto and faulted” state; andremoving data for the “auto and maintenance” states and data from the“auto and faulted” states from the collected operation data prior to thestep of removing data for the OFF states.
 12. A method for analyzingoperation of at least one machine, comprising: collecting operation datafor a machine over a plurality of predetermined time periods, theoperation data including the time for cycle events, starve events,blocked events, and down events; determining for each of thepredetermined time periods whether the machine is in an “ON” state or an“OFF” state based at least in part on the collected operation data;removing data for the OFF states from at least a portion of thecollected operation data, thereby generating a filtered data set;determining a time-to-failure parameter using at least the down eventsfrom the filtered data set; determining a time-to-repair parameter usingat least the down events from the filtered data set; choosing aprobability density function; and fitting the determined parameters tothe chosen probability density function, thereby generating reliabilityinformation for the machine to facilitate predictions of future machineoperation.
 13. The method of claim 12, further comprising: collectingadditional operation data for the machine over a plurality of additionalpredetermined time periods; determining for each of the additional timeperiods whether the machine is in an ON state or an OFF state based atleast in part on the additional collected operation data; removing datafor the OFF states from at least a portion of the additional collectedoperation data, thereby generating an additional filtered data set;aggregating the filtered data set and the additional filtered data set,thereby generating a new filtered data set; determining a newtime-to-failure parameter using at least the down events from the newfiltered data set after the machine has had a failure; determining a newtime-to-repair parameter using at least the down events from the newfiltered data set after the failure has been repaired; determiningwhether the new determined parameters should be fit to the chosenprobability density function or another probability density functionchosen from a predetermined list of probability density functions; andfitting the new determined parameters to one of the probability densityfunctions, thereby generating reliability information for the machine tofacilitate predictions of future machine operation.
 14. The method ofclaim 13, wherein the time-to-repair parameter and the additionaltime-to-repair parameter are each a mean time-to-repair value, and thetime-to-failures parameter and the additional time-to-failure parameterare each a mean time-to-failure.
 15. The method of claim 12, wherein themachine is considered to be in an ON state for a given one of thepredetermined time periods when there is more than one occurrence of acycle event, a starve event, a blocked event, or a combination thereofduring the given predetermined time period.
 16. The method of claim 15,further comprising: determining for each of the predetermined timeperiods whether the machine is in an “auto and maintenance” state;determining for each of the predetermined time periods whether themachine is in an “auto and faulted” state; and removing data for the“auto and maintenance” states and data from the “auto and faulted”states from the collected operation data prior to the step of removingdata for the OFF states.
 17. The method of claim 12, the machine beingpart of a work area including a plurality of other machines, the methodfurther comprising: collecting operation data for the other machinesover the predetermined time periods, the operation data for the othermachines including the time for cycle events, starve events, blockedevents, and down events for each machine; determining for each of theother machines over each of the predetermined time periods whether theother machine is in an ON state or an OFF state based at least in parton the collected operation data; and determining for each of thepredetermined time periods whether the work area is in an ON state or anOFF state based at least in part on whether the machines in the workarea are in an ON state or an OFF state.
 18. The method of claim 17,wherein the work area is considered to be in an OFF state for a givenone of the predetermined time periods if at least half of the machinesin the work area are determined to be in an OFF state during the givenpredetermined time period.
 19. The method of claim 18, furthercomprising: removing additional data from at least a portion of thecollected operation data to generate the filtered data set, theadditional data removed including data for the ON states of the machinesduring a given one of the predetermined time periods when the work areais determined to be in an OFF state for the given predetermined timeperiod.
 20. The method of claim 19, further comprising: determining foreach of the machines a constraint parameter related to the time eachmachine is in an OFF state; and ordering each of the machines accordingto the determined constraint parameter, thereby providing informationregarding bottlenecks in the work area.
 21. A method for analyzingoperation of at least one machine, comprising: defining a work areahaving a plurality of machines; collecting corresponding operation datafor the machines over a plurality of predetermined time periods, theoperation data including the respective time for a plurality of eventsthat together form a set of mutually exclusive events that describeoperation of the machine, including the time for cycle events, starveevents, blocked events, and down events for each respective machine;determining for each of the machines over each of the predetermined timeperiods whether the respective machine is in an “ON” state or an “OFF”state based at least in part on the respective collected operation data;removing data for the OFF states from at least a portion of thecorresponding collected operation data for each machine, therebygenerating a filtered data set that includes information for eachmachine; and generating reliability information for each machine basedat least in part on the filtered data set, thereby facilitatingpredictions of future operation of each machine, the step of generatingreliability information for each machine including: determining areliability parameter for each machine based at least in part on thedown events for the respective machine in the filtered data set;choosing a corresponding probability density function for each machine;and fitting each of the reliability parameters to the respective chosenprobability density function.
 22. The method of claim 21, furthercomprising determining for each of the predetermined time periodswhether the work area is in an ON state or an OFF state based at leastin part on whether the machines in the work area are in an ON state oran OFF state, the work area being considered to be in an OFF state for agiven one of the predetermined time periods if a predeterminedpercentage of the machines in the work area are determined to be in anOFF state during the given predetermined time period.
 23. The method ofclaim 22, further comprising removing additional data from at least aportion of the collected operation data to generate the filtered dataset, the additional data removed including data for the ON states of themachines during a given one of the predetermined time periods when thework area is determined to be in an OFF state for the givenpredetermined time period.